On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes

15Citations
Citations of this article
19Readers
Mendeley users who have this article in their library.

Abstract

It is well known that the complexity, i.e. the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as Θ(n 2). It is also known that if the points are chosen Independently Identically Distributed uniformly from a 3-dimensional region such as a cube or sphere, then the expected complexity falls to O(n). In this paper we introduce the problem of analyzing what occurs if the points are chosen from a 2-dimensional region in 3-dimensional space. As an example, we examine the situation when the points are drawn from a Poisson distribution with rate n on the surface of a convex polytope. We prove that, in this case, the expected complexity of the resulting Voronoi diagram is O(n). © 2003 Elsevier Science B.V.

Cite

CITATION STYLE

APA

Golin, M. J., & Na, H. S. (2003). On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes. Computational Geometry: Theory and Applications, 25(3), 197–231. https://doi.org/10.1016/S0925-7721(02)00123-2

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free